Harmonic-trap critical-temperature prefactor
= Harmonic-trap critical-temperature prefactor
The ideal isotropic-trap transition scale is $T_0=\zeta(3)^{-1/3}(\hbar\omega/k_B)N^{1/3}$. The numerical prefactor $\zeta(3)^{-1/3}\simeq0.9405$ follows from the Bose integral $\int_0^\infty x^2/(e^x-1)\,dx=2\zeta(3)$.